What is the derivative of (x^7/7-x^3-3/x+1/(5x^5)) ?

The derivative of (x^7/7-x^3-3/x+1/(5x^5)) is x^6-3x^2+3/(x^2)-1/(x^6)

What is the first derivative of (x^7/7-x^3-3/x+1/(5x^5)) ?

The first derivative of (x^7/7-x^3-3/x+1/(5x^5)) is x^6-3x^2+3/(x^2)-1/(x^6)

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\frac{d}{d x} (\frac{x ^{7}}{7} - x^{3} - \frac{3}{x} + \frac{1}{5 x ^{5}})

x^{6} - 3 x^{2} + \frac{3}{x ^{2}} - \frac{1}{x ^{6}}

Solution steps

\frac{d}{d x} (\frac{x ^{7}}{7} - x^{3} - \frac{3}{x} + \frac{1}{5 x ^{5}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{x ^{7}}{7}) - \frac{d}{d x} (x^{3}) - \frac{d}{d x} (\frac{3}{x}) + \frac{d}{d x} (\frac{1}{5 x ^{5}})

\frac{d}{d x} (\frac{x ^{7}}{7}) = x^{6}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (\frac{3}{x}) = - \frac{3}{x ^{2}}

\frac{d}{d x} (\frac{1}{5 x ^{5}}) = - \frac{1}{x ^{6}}

= x^{6} - 3 x^{2} - (- \frac{3}{x ^{2}}) - \frac{1}{x ^{6}}

Simplify

= x^{6} - 3 x^{2} + \frac{3}{x ^{2}} - \frac{1}{x ^{6}}

What is the derivative of (x^7/7-x^3-3/x+1/(5x^5)) ?
The derivative of (x^7/7-x^3-3/x+1/(5x^5)) is x^6-3x^2+3/(x^2)-1/(x^6)
What is the first derivative of (x^7/7-x^3-3/x+1/(5x^5)) ?
The first derivative of (x^7/7-x^3-3/x+1/(5x^5)) is x^6-3x^2+3/(x^2)-1/(x^6)